Dynamically screened electron–electron scattering in two dimensions

The properties of dynamically screened electron–electron interactions in a two-dimensional and quasi-two-dimensional semiconductor are described analytically for the situation where the electron gas obeys classical statistics. The electron–electron interaction is taken to be screened by the polar lattice and by free electrons in the lowest subband. The character of the screening is shown to be critically dependent on the energy and momentum exchanged in the electron–electron interaction. A remarkable feature is the resonant enhancement of the interaction strength by coupled-phonon–plasmon mode effects. As a consequence, the coupled-mode enhancement of the electron–electron energy exchange rate offers substantial competition to the energy-relaxation rate of electrons via optical-phonon emission.